At our institute, we have several Macs (from 10.6 to 10.8) but not one is running a server version. In the one running 10.8 there are 4.5 TB of hard-drives from which 2 x 2 TB are raided together (mirrored) with to goal to use them as a Time Machine backup for all other Macs. All the Macs are connected over the institute network.

Now, how do I set up everything such that all Macs can use Time Machine to backup to this one Mac?

I've read that this might be easier when the target Mac would run OS X Server.

This might work better to flip around the question. What devices can configured to look like Time Capsule / OS X server so that Macs will back up to it. Server is more like installing a database that runs on top of OS X than a total wipe and reinstall as in days past. I'll spruce up the answer to use OS X in case you were unaware of how it works on Mountain Lion.
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bmike♦Feb 7 '13 at 18:08

This isn't an answer to your question as phrased, it's a) information and b) an alternative. A = The experiences I have heard from people who use Time Capsule is not good, those who use Time Machine over a network drive all said it eventually corrupted or was too slow so they gave it up. B = Consider CrashPlan as a free alternative. It is designed to work this way, over a LAN or even the Internet. I have been using it quite happily for several months between OS X 10.8 (non-server) Macs. FWIW.
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TJ LuomaAug 7 '13 at 6:23

It will allow you to select any network drive from System Preferences: Time Machine.

The network drive should be a HFS+ file system over AFP (standard file sharing from another Mac). I would strongly discourage you from using any other setup if you are not prepared to manually restore one file at a time from the backup.

If that doesn't work for you, or you need more configuration options, install OS X Server. It's an officially supported feature, and Server only costs $20 from the Mac App Store. Unlike older versions, Server for 10.8 is just an MAS install and doesn't require reinstalling the OS.

Side note: do not ever use the TMShowUnsupportedNetworkVolumes option if you value the integrity of your backups. Unsupported volumes are unsupported for a reason: Time Machine requires certain specific file-sharing features to ensure that the backups aren't corrupted if, for example, the network connection drops in the middle of a backup. Enabling this option disables checking for those features and I have seen it result in corrupted backups quite a few times.

yes, OS X Server is pretty cheap but you need a mac hardware to install it, and it is not cheap at all
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pqnetAug 17 '13 at 0:01

@pqnet you don't need a high end Mac to run Server and some Time Machine backups. A low end Mac mini is more than enough. I have a C2D Mac mini from 2006 that is running an older version of Server (10.7) just fine. Just look around on eBay, Craigslist or wherever you can find old hardware for an older Mac that's capable of running the latest OS X version and get that.
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Dennis MunsieDec 26 '14 at 17:46

@DennisMunsie the cheapest solution is probably going to be a time capsule anyway. The mac os server is useful either for those who have a big number of computer to back up, for which the time capsule would not be powerful enough (such as the situation described here) or if you already have old mac hardware you wouldn't use anyway.
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pqnetJan 6 at 14:59

OS X Server is probably the best way to go. It is stable and easy to install over the Mac OS you have on destination mac.

There are inexpensive books less than $50 walking you through the entire server setup process, and the software itself is $20 in the US store.

It takes someone familiar with server an hour to set up a Mac to serve just Time Machine functionality, so the investment should be manageable for someone that wanted to save paying for help and learning to DIY and not being pressed for time so they can ask and search the net if issues crop up during setup.

I wanted to backup my MBA and MBP using a networked drive. I have a MacMini that I use as a media center. I installed OS X Server on the MacMini and using a regular 1 TB USB drive as the TimeCapsule disk.